Kit Malthouse has become the second Tory MP to pull out of the contest to replace Theresa May, after James Cleverly announced he was also pulling out.
Malthouse was considered an outsider in the race, in which 11 Tory MPs are now running.
Malthouse served as a deputy mayor to the frontrunner in the race, Boris Johnson, while a member of the London Assembly.
During the Brexit debate, he offered an alternative Brexit plan that later became known as the Malthouse compromise. It called for Prime Minister to replace the Irish backstop with a free trade agreement, with technology to prevent a hard border on the island of Ireland.
It also called for the transition period to be extended.
Announcing his decision on Twitter, Malthouse said: